How do you determine if the improper integral converges or diverges #int (1/(3x)-6) dx# from negative infinity to 0?
1 Answer
Explanation:
To evaluate a two-sided improper integral, split it into two integrals and express each as a limit like so:
Now compute the integrals and evaluate the limits:
Therefore the integral diverges as it approaches
Technically, we could stop here. If one integral diverges, the whole expression will diverge. But let's evaluate the second limit just for good measure:
And again we see the integral also diverges as it approaches 0.